Section 3.3 class notes_0 - Section 3.3 Graphs of Basic...

Section 3.3 Graphs of Basic Functions; Piecewise Functions Objective 1: Sketching the Graphs of the Basic Functions We begin by discussing the graphs of two specific linear functions. Recall that a linear function has the form ( ) f x mx b = + where m is the slope of the line and b represents the y-coordinate of the y-intercept. We start our discussion of the basic functions by looking at the constant function , that is, the linear function with 0m = , the graph of which is a horizontal line. 1. The Constant Function = ( ) f x b Notice that there are no arrows used at either end of the graph representing the constant function above. From this point forward in the text, unless the graph contains a definitive endpoint (shown by either an open dot or a closed dot) then it will be understood that the graph extends indefinitely in the same direction. The identity function defined by ( ) f x x = is another linear function with 1 m = and 0. b = It assigns to each number in the domain the exact same number in the range. 2.

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